Dentability and extreme points in Banach spaces

AbstractIt is shown that a Banach space E has the Radon-Nikodym property (equivalently, every bounded subset of E is dentable) if and only if every bounded closed convex subset of E is the closed convex hull of its strongly exposed points. Using recent work of Namioka, some analogous results are obtained concerning weak∗ strongly exposed points of weak∗ compact convex subsets of certain dual Banach spaces

States on pseudo effect algebras and integrals

We show that every state on an interval pseudo effect algebra $E$ satisfying some kind of the Riesz Decomposition Properties (RDP) is an integral through a regular Borel probability measure defined on the Borel $\sigma$-algebra of a Choquet simplex $K$. In particular, if $E$ satisfies the strongest type of (RDP), the representing Borel probability measure can be uniquely chosen to have its support in the set of the extreme points of $K.

On the number of Mather measures of Lagrangian systems

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest

Non-local model of hollow cathode and glow discharge - theory calculations and experiment comparison

General form of the non-local equation for an ionization source in glow discharge and hollow cathode 3D-simulation is formulated. It is a fundamental equation in a hollow cathode theory, which allows to make up a complete set of field equations for a self-consistent problem in a stationary glow discharge and a hollow cathode. It enables to describe adequately the region of negative glow and the hollow cathode effect. Here you can see first attempts to compare calculation results of electrical dependences (pressure - voltage) and experimental data, - under conditions of gradual appearance of the hollow cathode effect.Comment: 4 pages, 2 figure

The Lattice and Simplex Structure of States on Pseudo Effect Algebras

We study states, measures, and signed measures on pseudo effect algebras with some kind of the Riesz Decomposition Property, (RDP). We show that the set of all Jordan signed measures is always an Abelian Dedekind complete $\ell$-group. Therefore, the state space of the pseudo effect algebra with (RDP) is either empty or a nonempty Choquet simplex or even a Bauer simplex. This will allow represent states on pseudo effect algebras by standard integrals

Optimal measures and Markov transition kernels

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative entropy are defined using the Kullback-Leibler divergence, and for this reason optimal measures belong to a one-parameter exponential family. Measures within such a family have the property of mutual absolute continuity. Here we show that this property characterizes other families of optimal positive measures if a functional representing information has a strictly convex dual. Mutual absolute continuity of optimal probability measures allows us to strictly separate deterministic and non-deterministic Markov transition kernels, which play an important role in theories of decisions, estimation, control, communication and computation. We show that deterministic transitions are strictly sub-optimal, unless information resource with a strictly convex dual is unconstrained. For illustration, we construct an example where, unlike non-deterministic, any deterministic kernel either has negatively infinite expected utility (unbounded expected error) or communicates infinite information.Comment: Replaced with a final and accepted draft; Journal of Global Optimization, Springer, Jan 1, 201

Subsurface scientific exploration of extraterrestrial environments (MINAR 5): analogue science, technology and education in the Boulby Mine, UK

The deep subsurface of other planetary bodies is of special interest for robotic and human exploration. The subsurface provides access to planetary interior processes, thus yielding insights into planetary formation and evolution. On Mars, the subsurface might harbour the most habitable conditions. In the context of human exploration, the subsurface can provide refugia for habitation from extreme surface conditions. We describe the fifth Mine Analogue Research (MINAR 5) programme at 1 km depth in the Boulby Mine, UK in collaboration with Spaceward Bound NASA and the Kalam Centre, India, to test instruments and methods for the robotic and human exploration of deep environments on the Moon and Mars. The geological context in Permian evaporites provides an analogue to evaporitic materials on other planetary bodies such as Mars. A wide range of sample acquisition instruments (NASA drills, Small Planetary Impulse Tool (SPLIT) robotic hammer, universal sampling bags), analytical instruments (Raman spectroscopy, Close-Up Imager, Minion DNA sequencing technology, methane stable isotope analysis, biomolecule and metabolic life detection instruments) and environmental monitoring equipment (passive air particle sampler, particle detectors and environmental monitoring equipment) was deployed in an integrated campaign. Investigations included studying the geochemical signatures of chloride and sulphate evaporitic minerals, testing methods for life detection and planetary protection around human-tended operations, and investigations on the radiation environment of the deep subsurface. The MINAR analogue activity occurs in an active mine, showing how the development of space exploration technology can be used to contribute to addressing immediate Earth-based challenges. During the campaign, in collaboration with European Space Agency (ESA), MINAR was used for astronaut familiarization with future exploration tools and techniques. The campaign was used to develop primary and secondary school and primary to secondary transition curriculum materials on-site during the campaign which was focused on a classroom extra vehicular activity simulation

Artificial Intelligence for the Electron Ion Collider (AI4EIC)

The Electron-Ion Collider (EIC), a state-of-the-art facility for studying the strong force, is expected to begin commissioning its first experiments in 2028. This is an opportune time for artificial intelligence (AI) to be included from the start at this facility and in all phases that lead up to the experiments. The second annual workshop organized by the AI4EIC working group, which recently took place, centered on exploring all current and prospective application areas of AI for the EIC. This workshop is not only beneficial for the EIC, but also provides valuable insights for the newly established ePIC collaboration at EIC. This paper summarizes the different activities and R and D projects covered across the sessions of the workshop and provides an overview of the goals, approaches and strategies regarding AI/ML in the EIC community, as well as cutting-edge techniques currently studied in other experiments

Artificial Intelligence for the Electron Ion Collider (AI4EIC)

The Electron-Ion Collider (EIC), a state-of-the-art facility for studying the strong force, is expected to begin commissioning its first experiments in 2028. This is an opportune time for artificial intelligence (AI) to be included from the start at this facility and in all phases that lead up to the experiments. The second annual workshop organized by the AI4EIC working group, which recently took place, centered on exploring all current and prospective application areas of AI for the EIC. This workshop is not only beneficial for the EIC, but also provides valuable insights for the newly established ePIC collaboration at EIC. This paper summarizes the different activities and R and D projects covered across the sessions of the workshop and provides an overview of the goals, approaches and strategies regarding AI/ML in the EIC community, as well as cutting-edge techniques currently studied in other experiments